CNN has already picked two potential replacements for Parker, a Pulitzer Prize-winning conservative columnist with The Washington Post.

The favorite to land the chair next to Spitzer is E.D. Hill. She’s a former Fox News anchor and co-host of “Fox and Friends.”

Hill was pulled from Fox in the wake of the controversy surrounding her describing a celebratory fist-bump between Michelle and then-Sen. Barack Obama as a “terrorist fist jab” after an Obama primary victory in 2008.

She may have been auditioning last month when she filled in as a guest host for Parker.

The other name being tossed around is Will Cain, a writer for National Review, who is a frequent guest on Fox News.

“Parker Spitzer” debuted in October to dismal ratings and has been plagued by in-fighting.

The Post exclusively reported last month that Parker stormed off the set after complaining that Spitzer dominated the nightly gab-fest.

Things haven’t gotten any better on the set since that hissy-fit, the sources said.

“She’s been openly threatening to quit,” a source said last night.

But, insiders added, the show’s producers love the job Spitzer has been doing for the show.

The sources earlier called Spitzer — who once famously described himself as a “f – – – ing steamroller” who would crush his political opponents — as “smart” and “tenacious” and said that he’s “turned out better” than they expected.

Staffers griped that Parker seemed like a wilting flower next to the hard-charging former state attorney general, who resigned as governor in 2008 after admitting he patronized a high-price hooker ring.